Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 30, Problem 42P
To determine
Derive an equation for neutron mass by considering head on collisions of neutrons with two stationary target nucleus.
To determine
The mass of the neutron found using the above expression.
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Po-204 (mass=204 amu) undergoes alpha decay. Show that, as a
result of ejecting alpha particle (He-4, mass=4 amu), the daughter
nucleus recoils with a speed equal to 2 % that of the alpha particle.
Po
Po-204 (mass=204 amu) undergoes alpha decay. Show that, as a result of ejecting alpha particle (He-4, mass=4 amu), the daughter nucleus recoils with a speed equal to 2 % that of the alpha particle.
Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (19 Au). The energy of
the incoming helium nucleus was 7.35 x 10
-13 j, and the masses of the helium and gold nuclei were 6.68 x 10-27 kg and 3.29 x 10-25
kg, respectively (note that their mass ratio is 4 to 197. Assume that the helium
nucleus travels in the +x-direction before the collision.)
(a) If a helium nucleus scatters to an angle of 112° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise
from the +x-axis) of the gold nucleus.
120°
He nucleus
Gold nucleus
4He speed
m/s
197Au velocity
m/s
197
Au direction
° counterclockwise from the +x-axis
(b) What is the final kinetic energy (in J) of the helium nucleus?
J
Chapter 30 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 30.1 - Prob. 30.1QQCh. 30.1 - Prob. 30.2QQCh. 30.3 - Prob. 30.3QQCh. 30.3 - Suppose you have a pure radioactive material with...Ch. 30.4 - Which of the following is the correct daughter...Ch. 30.4 - Which of the following is the correct daughter...Ch. 30 - Prob. 1OQCh. 30 - Prob. 2OQCh. 30 - Prob. 3OQCh. 30 - Prob. 4OQ
Ch. 30 - Prob. 5OQCh. 30 - Prob. 6OQCh. 30 - Prob. 7OQCh. 30 - Prob. 8OQCh. 30 - Prob. 9OQCh. 30 - Prob. 10OQCh. 30 - Which of the following quantities represents the...Ch. 30 - Prob. 12OQCh. 30 - Prob. 1CQCh. 30 - Prob. 2CQCh. 30 - Prob. 3CQCh. 30 - Prob. 4CQCh. 30 - Prob. 5CQCh. 30 - Prob. 6CQCh. 30 - Prob. 7CQCh. 30 - If no more people were to be born, the law of...Ch. 30 - Prob. 9CQCh. 30 - Prob. 10CQCh. 30 - Prob. 11CQCh. 30 - What fraction of a radioactive sample has decayed...Ch. 30 - Prob. 13CQCh. 30 - Prob. 14CQCh. 30 - Prob. 15CQCh. 30 - Prob. 16CQCh. 30 - Prob. 17CQCh. 30 - Prob. 1PCh. 30 - Prob. 2PCh. 30 - Prob. 3PCh. 30 - Prob. 4PCh. 30 - Prob. 5PCh. 30 - Prob. 6PCh. 30 - Prob. 7PCh. 30 - Prob. 8PCh. 30 - Prob. 9PCh. 30 - Prob. 10PCh. 30 - Prob. 11PCh. 30 - Prob. 12PCh. 30 - Prob. 13PCh. 30 - Prob. 14PCh. 30 - Prob. 16PCh. 30 - Prob. 17PCh. 30 - Prob. 18PCh. 30 - What time interval elapses while 90.0% of the...Ch. 30 - Prob. 20PCh. 30 - Prob. 21PCh. 30 - Prob. 22PCh. 30 - Prob. 23PCh. 30 - Prob. 24PCh. 30 - Prob. 25PCh. 30 - Prob. 26PCh. 30 - Prob. 27PCh. 30 - Prob. 28PCh. 30 - Prob. 29PCh. 30 - Prob. 30PCh. 30 - Prob. 31PCh. 30 - Prob. 32PCh. 30 - Prob. 33PCh. 30 - Prob. 34PCh. 30 - Prob. 35PCh. 30 - Prob. 36PCh. 30 - Prob. 37PCh. 30 - Prob. 38PCh. 30 - Prob. 39PCh. 30 - Prob. 41PCh. 30 - Prob. 42PCh. 30 - Prob. 43PCh. 30 - Prob. 45PCh. 30 - Prob. 46PCh. 30 - Prob. 47PCh. 30 - Prob. 48PCh. 30 - Prob. 49PCh. 30 - Prob. 50PCh. 30 - Prob. 51PCh. 30 - Prob. 52PCh. 30 - Prob. 53PCh. 30 - Prob. 54PCh. 30 - Prob. 55PCh. 30 - Prob. 56PCh. 30 - Prob. 57PCh. 30 - Prob. 58PCh. 30 - Prob. 59PCh. 30 - Prob. 60PCh. 30 - Prob. 61PCh. 30 - Prob. 62PCh. 30 - Prob. 63PCh. 30 - Prob. 64PCh. 30 - Prob. 65PCh. 30 - Prob. 66PCh. 30 - Prob. 67PCh. 30 - Prob. 68PCh. 30 - Prob. 69PCh. 30 - Prob. 70P
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- Po-204 (mass=204 amu) goes alpha decay. Show that, as a result of ejecting alpha particle (He-4, mass=4 amu), the daughter nucleus recoils with a speed equal to 2% that of the alpha particle.arrow_forwardA stationary nucleus of Po-204 (mass = 204 amu) undergoes alpha decay. Show that, as a result of ejecting alpha particle (He-4: mass = 4 amu), the daughter nucleus recoils with a speed equal to 2% that of the alpha particle.arrow_forwardRutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2.2 ✕ 107 m/s and a mass of 6.7 ✕ 10−27 kg. Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision.arrow_forward
- A 212^Bi (bismuth) nucleus undergoes alpha decay, resulting in a 208^Tl (thallium) nucleus and a 4He (helium) nucleus as per the following reaction: 212^Bi →208^Tl + 4^He The masses of each nucleus is listed in the table below. Given that the bismuth atom was at rest before the reaction, if the resulting thallium nucleus is traveling 3.3 × 105 m/s, how fast is the helium nucleus traveling?arrow_forwardTo estimate the mass mn of neutron Chadwick directed beam of projectile neutrons all having the same velocity at two different targets of hydrogen and nitrogen. The projectile neutrons after hitting the target nuclei made them to recoil. Answer the following questions. (a) If the maximum recoil speeds of the targets are denoted by vy and VN then show that PN-PH mn = Where PN and Py are momenta of the targets. (b) Assume the measured speeds of the targets were vy = 3.3 × 10’m/s, vN = 4.7 × 106 m/s. Using these data estimate the value for mnarrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.52 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 139° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. What is the final kinetic energy (in J) of the helium nucleus?arrow_forward
- Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (ªHe) from gold-197 nuclei (197 Au). The energy of the incoming helium nucleus was 7.28 × 10-13 J, and the masses of the helium and gold nuclei were 6.68 × 10-27 kg and 3.29 × 10-25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a) If a helium nucleus scatters to an angle of 136° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed 197 Au velocity t 197 Au direction 14500000 0.0140 -17 m/s X m/s ° counterclockwise from the +x-axis (b) What is the final kinetic energy (in J) of the helium nucleus? 7.02e-13 Jarrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.27 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a) If a helium nucleus scatters to an angle of 148° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus 4He speed: (m/s) 197Au velocity (m/s) 197Au direction (counterclockwise from the +x-axis) (b)What is the final kinetic energy (in J) of the helium nucleus?arrow_forwardRutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2.4 ✕ 107 m/s and a mass of 6.7 ✕ 10−27 kg.Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision. ?m/sarrow_forward
- Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.12 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg,respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 119° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed ______m/s 197Au velocity____ m/s 197 Au direction 330.36 ° counterclockwise from the +x-axis (b)What is the final kinetic energy (in J) of the helium nucleus? ___________ Jarrow_forwardRutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2.4 ✕ 107 m/s and a mass of 6.7 ✕ 10−27 kg. Assume the alpha particle collided with a gold nucleus that was initially at rest. Find the speed of the nucleus after the collision. m/sarrow_forwardErnest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (4He) from gold-197 nuclei (197Au). The energy of the incoming helium nucleus was 7.12 ✕ 10−13 J, and the masses of the helium and gold nuclei were 6.68 ✕ 10−27 kg and 3.29 ✕ 10−25 kg,respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.) (a)If a helium nucleus scatters to an angle of 119° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus. 4He speed_____________ m/s 197Au velocity _____________ m/s 197Au direction____________ ° counterclockwise from the +x-axis (b)What is the final kinetic energy (in J) of the helium nucleus? ______________ Jarrow_forward
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